Blair, who left office in 2007, said Andy Burnham's government should be clear it wants to enter into a "structured formal relationship" where "everything is on the table".
Blair said the EU inviting Canada to become its first associate member showed a "newfound flexibility" in relations between the EU and non-member states.
However, the former Labour leader said it would be wrong to return to a straight membership of the single market and customs union. In a slight to the leadership of Keir Starmer, he also cautioned towards an "inching towards" Europe as a result of public opinion.
The report said Britain rejoining a "significantly reformed" EU, along with reforms inside the bloc, could see Europe as a superpower that could challenge the US and China.
"Britain should play a leading role in shaping a more powerful Europe. The necessary reforms have already been identified - not least in Mario Draghi's report on EU competitiveness - but implementing them remains the challenge," it said.
"For Britain to be part of that effort, it must show political commitment to Europe. This can be achieved by setting a clear, public objective to rejoin the EU within a decade - subject to internal EU reform.
"This objective should be a cornerstone of the UK government's upcoming 10-year plan."
In the foreword to the report entitled Beyond Leave and Remain: A Path to Rejoining a Reformed Europe, Blair said: "The red lines which we drew in 2016 are not the same as 2026.
"We need a new approach which makes sense of the world as it has changed in this decade, and which treats our future relationship in Europe not as a question about whether Britain 'reverses' Brexit but about whether we can secure a modern relationship with Europe which is in our national interest today."
Polling by Best for Britain suggested Labour would get closest to forming a majority government at the next election by adopting a manifesto commitment to rejoining the EU.
A pledge to reverse Brexit was the only scenario tested that would stop a Reform UK-led government, according to the poll, which asked 13,400 adults.
On Thursday, a report by the Institute for Public Policy Research found UK goods exports to the EU would have been up to STG6.5 billion ($A12.2 billion) a year from 2021 to 2024 if Britain had got a mutual-recognition agreement in place.
Currently, some products undergo additional testing and certification before they can be sold in EU markets.
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